fdrinca Posted November 9, 2017 Share Posted November 9, 2017 Shower brainstorming this morning on trying to answer my daughter's question "but WHY do we multiply to find the part of the whole" had me realize that I should teach addition on number line (1 dimensional space) and multiplication in two dimensional space. I'm only starting to cogitate this, but anyone have a direction for me to head? Quote Link to comment Share on other sites More sharing options...
ondreeuh Posted November 9, 2017 Share Posted November 9, 2017 You can use cuisenaire rods or base-ten blocks to show it. Quote Link to comment Share on other sites More sharing options...
nixpix5 Posted November 10, 2017 Share Posted November 10, 2017 That is basically how Montessori does it using a strip board (number line) for addition and subtraction and once the child understands that multiplication is just a simplified way of adding sets then they use a multiplication board (an array) which is just a 2 dimensional quadrant essentially. Base ten blocks and rods serve this purpose just fine. 1 Quote Link to comment Share on other sites More sharing options...
fdrinca Posted November 10, 2017 Author Share Posted November 10, 2017 You can use cuisenaire rods or base-ten blocks to show it. That is basically how Montessori does it using a strip board (number line) for addition and subtraction and once the child understands that multiplication is just a simplified way of adding sets then they use a multiplication board (an array) which is just a 2 dimensional quadrant essentially. Base ten blocks and rods serve this purpose just fine. Thanks for your replies. I'm wondering specifically if there are materials where one of the factors is less than 1. For example, using two dimensional space to represent 1/6 of 20. Earlier today I explained to my son why we multiply a number by a percentage to find the percent of the number using this framework. (Sorry, math words are clunky - why 0.3 X 55 solves for 30% of 55) It was a lightbulb moment for him. Thinking in terms of finding the **area** of two numbers, rather than the **product** was eye-opening. Quote Link to comment Share on other sites More sharing options...
nixpix5 Posted November 10, 2017 Share Posted November 10, 2017 (edited) Thanks for your replies. I'm wondering specifically if there are materials where one of the factors is less than 1. For example, using two dimensional space to represent 1/6 of 20. Earlier today I explained to my son why we multiply a number by a percentage to find the percent of the number using this framework. (Sorry, math words are clunky - why 0.3 X 55 solves for 30% of 55) It was a lightbulb moment for him. Thinking in terms of finding the **area** of two numbers, rather than the **product** was eye-opening. Decimal checkerboard with multiplication is what is used to teach it concretely in Montessori. If you google you can probably find a tutorial video to get a sense of how it works. It is also taught with fraction circles, long division board and various other ways. My favorite though is checkerboard because kids can solve questions like ".35 × 49" for example in a fun, easy and visual way. I have seen kids completely get it and have "ah ha" moments with that material. It is spendy but I made my own pretty easily. You could watch a video on "multiplying fractions Montessori" and see how fraction circles are used in a similar way to show how an area or portion of a product is determined: https://www.google.com/url?sa=t&source=web&rct=j&url=https://m.youtube.com/watch%3Fv%3D8rmq0yz8FdU&ved=0ahUKEwj95u6cqbPXAhXMx4MKHdMuDBEQwqsBCCMwAA&usg=AOvVaw01YRhXJx50tv7rwr0ak1E5 Here she is using it in fraction notation but you could do this in decimal form as well multiplying whole numbers. If he understands that 2x4 is two sets of four then using that same language .25 x 4 is .25 sets of 4 (i.e. 25% of 4). I will see if I can find a checkerboard example... Edited November 10, 2017 by nixpix5 1 Quote Link to comment Share on other sites More sharing options...
ondreeuh Posted November 10, 2017 Share Posted November 10, 2017 Thanks for your replies. I'm wondering specifically if there are materials where one of the factors is less than 1. For example, using two dimensional space to represent 1/6 of 20. Earlier today I explained to my son why we multiply a number by a percentage to find the percent of the number using this framework. (Sorry, math words are clunky - why 0.3 X 55 solves for 30% of 55) It was a lightbulb moment for him. Thinking in terms of finding the **area** of two numbers, rather than the **product** was eye-opening. The Singapore method of using bar models does this. We use Math in Focus (newer version of SM) and this is how all operations are illustrated this way. To find 1/6 of 20, you would split the bar into 6 equal pieces. To find 1/3 of 1/4, you would split the bar into fourths, and then split each fourth into thirds, then count one of each third. 1 Quote Link to comment Share on other sites More sharing options...
Kiara.I Posted November 12, 2017 Share Posted November 12, 2017 (edited) This poster might be helpful too: https://naturalmath.com/multiplication-models-poster/ Sent from my ONEPLUS A5000 using Tapatalk Edited November 12, 2017 by Kiara.I Quote Link to comment Share on other sites More sharing options...
EKS Posted November 13, 2017 Share Posted November 13, 2017 Math U See, perhaps? Quote Link to comment Share on other sites More sharing options...
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